Details

sample541.0ms

Algorithm

intervals

Results

167.0ms	48×	body	2560	valid
117.0ms	92×	body	1280	valid
111.0ms	65×	body	640	valid
12.0ms	28×	body	320	valid
4.0ms	14×	body	160	valid
2.0ms	9×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

40.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
11.0ms	(- x (sin x))

series288.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (- x (sin x)) (- x (tan x)))
100.0ms	(- x (tan x))
68.0ms	(- x (sin x))

simplify753.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune405.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/ (sin x) (- x (tan x)))
107.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series476.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sin x) (- x (tan x)))
233.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
79.0ms	(- x (tan x))
67.0ms	(- x (tan x))

simplify745.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1452
1	389
0	177

prune520.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 2) (- 9/40 (* (pow x 2) 27/2800)))
0.2b	(* (pow x 2) 27/2800)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`associate-l`
12×	`add-exp-log`
8×	`unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt` `unswap-sqr`
6×	`add-cbrt-cube` `associate-r` `prod-exp`
4×	`unpow2` `sqr-pow`
2×	`distribute-rgt-in` `pow-to-exp` `pow1` `sub-neg` `distribute-lft-in` `pow-exp` `associate-r/` `-commutative` `cbrt-unprod` `add-log-exp`
1×	`flip3--` `flip--`

Counts

2 → 60

Calls

2 calls:

32.0ms	(* (pow x 2) (- 9/40 (* (pow x 2) 27/2800)))
15.0ms	(* (pow x 2) 27/2800)

series187.0ms

Counts

2 → 6

Calls

2 calls:

145.0ms	(* (pow x 2) (- 9/40 (* (pow x 2) 27/2800)))
42.0ms	(* (pow x 2) 27/2800)

simplify757.0ms

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
2	960
1	220
0	97

prune220.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
1.4b	(- (/ x (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (/ (- x (tan x)) (cbrt (sin x)))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
14×	`times-frac`
11×	`*-un-lft-identity`
10×	`add-log-exp` `difference-of-squares`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow1/3` `frac-sub`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (sin x))
91.0ms	(- (/ x (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (/ (- x (tan x)) (cbrt (sin x)))))
8.0ms	(- x (tan x))
9.0ms	(- x (tan x))

series576.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (sin x))
234.0ms	(- (/ x (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (/ (- x (tan x)) (cbrt (sin x)))))
97.0ms	(- x (tan x))
87.0ms	(- x (tan x))

simplify644.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1193
1	346
0	149

prune468.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch100.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.03735179155868629
7	-0.10952899301968014	-0.00181011214377754	-0.03488869783196479

simplify3.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample14.1s

Algorithm

intervals

Results

6.9s	1679×	body	2560	valid
3.6s	2685×	body	1280	valid
1.9s	1884×	body	640	valid
1.1s	902×	body	320	valid
190.0ms	496×	body	160	valid
73.0ms	354×	body	80	valid